Modelling and estimating heavy-tailed non-homogeneous correlated queues: Pareto-inverse gamma HGLM with covariates

Abstract

Evidence of communication traffic complexity reveals correlation in a within-queue and heterogeneity among queues. We show how a random-effect model can be used to accommodate these kinds of phenomena. We apply a Pareto distribution for arrival (service) time of individual queue for given arrival (service) rate. For modelling potential correlation in arrival (service) times within a queue and heterogeneity of the arrival (service) rates among queues, we use an inverse gamma distribution. This modelling approach is then applied to the cache access log data processed through an Internet server. We believe that our approach is potentially useful in the area of network resource management.

Keywords:

• Within-queue correlation
• between-queue variability
• internet traffic
• random effects linear model
• hierarchical generalized linear model